The sine theorem and inequalities for volumes of simplices and determinants
type: Item
instance of: scholarly article
title: The sine theorem and inequalities for volumes of simplices and determinants
zbMATH Open document ID: 0824.51015
DOI: 10.1016/0024-3795(93)00196-7
author: Darko Veljan
published in: Linear Algebra and its Applications
publication date: 1995-05-23T00:00:00Z
review text: The author provides two simple proofs of the sine theorem for \(n\)- dimensional simplices, which is used, together with an inequality of L. Fejes Tóth, to prove a volume majorization for an \(n\)-simplex in terms of the \((n-1)\)-dimensional content of its faces. Several corollaries are proved, one of them providing a volume majorization for an \(n\)-simplex in terms of the distances between its vertices. This corollary can be regarded as an improvement of the Hadamard (1893) inequality. Given that most of these results are known, the main merit of the present paper lies in the presentation of self-contained elementary proofs.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 757609
zbMATH Keywords: sine theorem
zbMATH Keywords: simplices
zbMATH Keywords: inequality
zbMATH Keywords: volume
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00196-7
OpenAlex ID: W2061748236
cites work: The sine theorem for simplexes in $E_n$
cites work: Determinantensätze und Simplexeigenschaften (Verallgemeinerung trigonometrischer Lehrsätze auf n‐dimensionale Simplexe)
cites work: The law of sines for tetrahedra and \(n\)-simplices
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cites work: A generalisation to several dimensions of the Neuberg-Pedoe inequality, with applications
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Wikidata QID: Q126657490
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description: scientific article; zbMATH DE number 757609